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NON-STANDARD ANALYSIS AND MULTIPLICATION OF DISTRIBUTIONS

Bin Li

1978Mathematics被引 27

摘要

The problem of multiplication of distributions is, as we know, one which has not yet been solved satisfactorily. Using non-standard analysis in this paper, we give a multiplication which is defined for any two distributions and ineindes standard multiplications of a great variety as the particular eases. We have calculated δ~((m))(x)·δ((n))(x), δ((m))(x)·x~(-n), θ(x)·x~(-n), etc. These formulae of products are possibly significant for quantum field theory. In this paper, we apply the notion of order of a distribution at a point to give a standard mulfiplication which is very broad. Moreover, in this paper we cite instances to illustrate that many well-known results about multiplication may be obtained very concisely by our method.

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